Stochastic Discrete-Time Process
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A Stochastic Discrete-Time Process is a stochastic process that is a discrete-time process (characterized by randomness or uncertainty in its state transitions).
- Context:
- It can be modeled using a Discrete-Time Stochastic Model that utilizes probability distributions for state transitions.
- It can range from being a First-Order Stochastic Discrete-Time Process to higher-order processes where future states depend on a sequence of previous states.
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- Example(s):
- a Markov Chain, such as:
- The price of a stock at the close of each trading day (can be modeled with a first-order Markov chain).
- a Queuing System, such as:
- The number of people in a line at a checkout counter (can be modeled using a Poisson process over discrete time intervals).
- a Random Walk, such as:
- The position of a particle undergoing random motion in a one-dimensional space (can be modeled as a first-order stochastic discrete-time process).
- a Hidden Markov Model, such as:
- In speech recognition, where the observable data depends probabilistically on the hidden state (itself following a Markov process).
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- a Markov Chain, such as:
- Counter-Example(s):
- a Deterministic Discrete-Time Process, where future states are entirely determined by current states.
- a Continuous-Time Stochastic Process, where randomness is embedded in a continuous time framework.
- See: Stochastic Process, Discrete-Time Process, Markov Chain, Queuing Theory.